v=9/10v+6=11

Solution for v=9/10v+6=11 equation:

v=9/10v+6=11

We move all terms to the left:

v-(9/10v+6)=0


Domain of the equation: 10v+6)!=0

v∈R


We get rid of parentheses

v-9/10v-6=0

We multiply all the terms by the denominator


v*10v-6*10v-9=0

Wy multiply elements

10v^2-60v-9=0

a = 10; b = -60; c = -9;
Δ = b2-4ac
Δ = -602-4·10·(-9)
Δ = 3960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3960}=\sqrt{36*110}=\sqrt{36}*\sqrt{110}=6\sqrt{110}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{110}}{2*10}=\frac{60-6\sqrt{110}}{20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{110}}{2*10}=\frac{60+6\sqrt{110}}{20}
$